Yes, when I fish electric only waters, I use the group 24 DEEP CYCLE battery for the ONIX and 360 only. I use two group 27 batteries for my bow 24V motor and two group 27 batteries for my transom 24V motor.
When I fish waters using my outboard, I use one of the group 27 batteries for engine starting and the electronics and the same two group 27 batteries for the bow trolling motor.
For several years, I used a 36V bow trolling motor and that involved another group 27 DEEP CYCLE battery.
The BRAND of battery you are using may be the issue. Get one that can handle the task, obviously the one you have cannot. What a lot were doing with the issue you have if they have a large outboard is use a Sears PM-1 size 31 which is a Dual Purpose for starting and deep cycle use for electonics, pumps, lights, etc. That battery is no longer available so a similar one is used OR two batteries parallel for the task.
This is my setup when using the outboard:
That lake is why I changed to a 24V bow motor to lighten the boat so stumps would not be as much of an issue.
There are thousands just below the surface. Been getting hung up on them for 20+ years.
One more thing is the power connection you use for the units. Each power cord should be extended directly to the battery with at least 14 gauge for the 1197 and 10 gauge for the ONIX. If you used the boat wiring harness, that is typically not enough for the load over distance. It's that resistance thing.